Unified semiclassical dynamics for molecular resonance spectra

Publisher Website
Google Scholar
Abstract
A method is presented to depict the intramolecular dynamics of resonantly coupled vibrations, starting from the experimental overtone and combination spectrum. The nonlinear least‐squares fit of the spectrum is used to obtain a semiclassical phase space Hamiltonian via the Heisenberg correspondence principle. This integrable Hamiltonian, corresponding to quasiperiodic motion, is used to generate a classical trajectory in phase space for each energy level in a resonance polyad. Polyad phase space profiles are shown to have complete mutual consistency starting from a fit in either the local or normal representation. It is argued that the best way to depict the phase space profile is on a spherical surface called the polyad phase sphere. Represented in this way, the local and normal mode phase spaces are seen to be a single entity, manifestly equivalent by a 90° rotation. The phase space trajectories can be converted into a coordinate space representation. This gives an easily visualized picture of the semiclassical intramolecular dynamics corresponding to each energy level. The polyad phase spheres from the fits of the experimental stretching spectra of H2O, O3 and SO2 are displayed. H2O and O3 are seen to be molecules with a local to normal modes transition, while SO2 is seen to be very near the pure normal modes limit. The experimentally determined phase space dynamics of H2O seen on the phase sphere are compared with the dynamics determined by Lawton and Child from trajectory calculations on the Sorbie–Murrell potential surface. The coordinate space trajectories corresponding to the phase spheres are compared with wave functions from the fit of the spectrum.